Q 11-12-125JEE MainJEE Main 2020 (8 Jan, Shift 1)Medium
The plot that depicts the behaviour of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature ($T$), qualitatively, is: (Graphs are schematic and not drawn to scale)
Answer: (C) see figure
$\tau = \dfrac{\lambda}{\bar v}$. For a fixed amount of gas in a fixed volume, the number density and hence the mean free path $\lambda = \dfrac{1}{\sqrt2\pi d^2n}$ do not depend on $T$, while $\bar v \propto \sqrt T$.
$$\tau \propto \frac{1}{\sqrt T}$$
So $\tau$ plotted against $\dfrac{1}{\sqrt T}$ is a straight line through the origin, i.e. graph (3).
Solution by Sreeraj P, M.Sc Physics